The widow is in the small shack with the brahmin pen just southwest of the sheriff's office. If you go talk to her about her plight you can either kick her out like the sheriff told you or you can pay the $120 of back rent she owes. If you pay the back rent you receive 1500 XP as your reward, and you gain 25 karma. However, if you evict her, you get 1500 XP and $100, but you lose 25 karma.